Question

Which of the following represent(s) an equation of the line passing through the points A(5, 6) and B(4, 8). Select all that apply.

Answer 1

For this case we have that the equation of a straight line in the form of an intersection is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We found the slope:

`m = \frac {y2-y1} {x2-x1} = \frac {8-6} {4-5} = \frac {2} {- 1} = - 2`

So, the line is:

`y = -2x + b`

We find the cut point by substituting a point:

`8 = -2 (4) + b\\8 = -8 + b\\b = 8 + 8\\b = 16`

Finally, the equation is:

`y = -2x + 16`

We can also have the equation of the point-slope form:

`y-y_ {0} = m (x-x_ {0})`

Where:

`(x_ {0}, y_ {0}) = (4,8)`represents a point:

So:

`y-8 = -2 (x-4)`

ANswer:

`y-8 = -2 (x-4)\\y = -2x + 16`